Productivity of $[\mu, \lambda ]$-compactness

TL;DR

This paper characterizes when $[, ]$-compactness is productive for certain singular cardinals, linking it to strong limit and strong compactness properties.

Contribution

It provides a precise criterion for the productivity of $[, ]$-compactness involving strong limit singular cardinals and their relation to -strong compactness.

Findings

Productivity of $[, ]$-compactness is characterized by  being -strongly compact.

If  b0 , then $[, ]$-compactness is productive.

The result applies when  b0  is a strong limit singular cardinal.

Abstract

We show that if $\mu \leq \cf \lambda $ and $\lambda$ is a strong limit singular cardinal, then $[\mu, \lambda ]$-compactness is productive if and only if either $\mu= \omega $, or $\mu$ is $\lambda$-strongly compact.